Jump Search
Jump Search works on sorted arrays by jumping ahead by fixed steps and then performing linear search in the identified block.
IntermediateTime: O(√n)Space: O(1)
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## How Jump Search Works
Jump Search is a searching algorithm for sorted arrays. It works by jumping ahead by fixed steps and then performing a linear search once the block containing the target is found.
### Algorithm Steps:
1. Calculate the optimal jump size: √n
2. Jump ahead by this size until finding a value >= target
3. Perform linear search in the identified block
4. Return the index if found, -1 otherwise
### Key Characteristics:
- **Requires sorted array**: Must be sorted before searching
- **Block-based**: Divides array into blocks of size √n
- **Optimal jump size**: √n provides the best balance
- **Better than linear**: O(√n) vs O(n) for linear search
Time & Space Complexity
| Case | Time Complexity |
|---|---|
| Best | O(1) |
| Average | O(√n) |
| Worst | O(√n) |
| Space | O(1) |
Practice Problems
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